Perimeter of quadrilateral inscribed in circle

Since PQR is an equilateral triangle inscribed in a circle of radius $r$, its side length $PQ = QR = PR = r\sqrt{3}$. Since PS is a diameter, $\angle PQS = 90^\circ$ and $\angle PRS = 90^\circ$. In right $\Delta PQS$, $QS = \sqrt{PS^2 - PQ^2} = \sqrt{(2r)^2 - (r\sqrt{3})^2} = \sqrt{4r^2 - 3r^2} = r$. Similarly, $RS = r$. Perimeter of quadrilateral PQSR $= PQ + QS + RS + RP = r\sqrt{3} + r + r + r\sqrt{3} = 2r + 2r\sqrt{3} = 2r(1 + \sqrt{3})$.